Question

Which of the following is a true statment?
(a) $\mathrm{\pi }\mathrm{and}\frac{22}{7}$are both rationals
(b) $\mathrm{\pi }\mathrm{and}\frac{22}{7}$are both irrationals
(c) $\mathrm{\pi }$ is rational and $\frac{22}{7}$is irrational
(d) $\mathrm{\pi }$ is irrational and $\frac{22}{7}$is rational

Answer 1

(d) $\mathrm{\pi }$ is irrational and $\frac{22}{7}$ is rational.
Because the value of $\mathrm{\pi }$ is neither repeating nor terminating, it is an irrational number. $\frac{22}{7}$, on the other hand, is of the form $\frac{p}{q}$, so it is a rational number.